Quiz At Home

Title: Calculus

Grade: Core-SAT3 Lesson: S6-P1

Explanation: Hello Students, time to practice and review. Let us take next 10-15 minutes to solve the ten problems using the Quiz Sheet. Then submit the quiz to get the score. This is a good exercise to check your understanding of the concepts.

Quiz: at Home

Problem Id Problem Options

1

Use the Square Root Property to solve the equation \$ 7(6x−1)^2 − 63 = 0 \$.

A) \$ x = 3, x = - 2 \$

B) \$ x = 2/3, x = - 1/3 \$

C) \$ x = - 2/3, x = - 1/2 \$

D) \$ x = 3/2, x = 1/2\$

2

Given the polynomial function \$ f(x) = 3x^2 − 5x + 2\$, find the roots of the equation f(x)=0.

A) \$ x = 3/2, x = 2\$

B) \$ x = 2/3, x = 1/3\$

C) \$ x = 2/3, x = 1\$

D) \$ x = - 3/2, x = - 1/2\$

3

Solve the equation: \$(2x^2 - 5x + 3)/(x - 1) = (x^2 - 2x - 3)/(x + 2)\$.

A) \$ (- 3 + \sqrt21)/2, (- 3 - \sqrt21)/2\$

B) \$ (3 + \sqrt21)/2, (3 - \sqrt21)/2\$

C) \$ 3 + \sqrt21, 3 - \sqrt21\$

D) \$ - 3 + \sqrt21, - 3 - \sqrt21\$

4

Find the limit of h(x) as x approaches infinity, where
\$h(x) = (2x^3 + 5x^2 - 3) / (3x^3 - x + 1)\$.

A) \$ 3/2\$

B) \$ 11/2 \$

C) \$ 9/5\$

D) \$2/3 \$

5

Evaluate the following:
\$\lim_{x \to 0} 5/x^3 \$

A) 5

B) \$ 125 \$

C) \$ \infty \$

D) 0

6

Factorize the quadratic expression:
\$ 16 z^2 - 40 z + 25 \$

A) \$ (5z + 4)^2\$

B) \$ (5z - 4)^2\$

C) \$ (4z + 5)^2\$

D) \$ (4z - 5)^2\$

7

Determine the degree and leading coefficient, of the polynomial function r(x) = \$ 4 x^5 - 2 x^4 + 7 x^3 - 3 x^2 + 2 x - 1\$.

A) Degree = 4 and Leading Coefficient = 5

B) Degree = 5 and Leading Coefficient = 4

C) Degree = 3 and Leading Coefficient = 2

D) Degree = 2 and Leading Coefficient = 3

8

Find the roots of the cubic function \$f(x) = x^3 - 6x^2 + 11x - 6\$.

A) x = 1, x = 2, x = 3

B) x = 2, x = 3, x = 4

C) x = 3, x = 4, x = 5

D) x = - 1, x = 2, x = 3

9

Solve this equation:
\$( 4x^2 - 7x + 3 )/(3x - 1) \$ = 0

A) x = 1 and x = - \$3/5\$

B) x = - 1 and x = \$3/2\$

C) x = 1 and x = - \$3/4\$

D) x = 1 and x = \$3/4\$

10

Determine if the function t(x) = \$ (x^3 - 2x^2 + 5x - 1 )/( 2x^2 - x + 3 ) \$ is continuous at x = 1.

A) No

B) Can’t be determined

C) Yes

D) Not applicable


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